Automated frequency tuning often seeks to match a load impedance presented to a generator to an impedance into which a generator is designed to deliver power. In some instances this can be accomplished by minimizing the magnitude of a load reflection coefficient, ρ, defined as
                    ρ        =                              z            -                          z              0                                            z            +                          z              0              *                                                          Equation        ⁢                                  ⁢                  (          1          )                    
where Z is the load impedance presented to the generator, Z0 is the desired load impedance and * indicates taking the complex conjugate. In many applications Z0=Z0*=50Ω.
Automated tuning algorithms sometimes gravitate to a local optimum and thereby miss a global optimum. FIG. 8 illustrates a plot of a measure of performance (e.g. reflected power or load reflection coefficient magnitude) as a function of frequency showing a local minimum at f1 and a global minimum at f0. In this illustration finding the optimum is equivalent to finding the minimum of the measure of performance. One can see that if the automated frequency tuning begins at a lower frequency than fa, then the algorithm is likely to settle in the local minimum at f1 and be unaware of the global minimum at f0.
For simple loads it is possible to simply sweep the frequency over the entire frequency range to find the global optimum at f0. In plasma applications such an approach to finding the global optimum frequency is often not an option. One potential problem is that as the frequency is swept, frequencies such as fa in FIG. 8, may be encountered where the load impedance is badly mismatched to the impedance into which the generator can deliver power. If the generator frequency dwells for any amount of time at such a frequency where the generator cannot deliver sufficient power into the load, the plasma may extinguish. If short periods of high reflected power are acceptable, then a technique of probing the entire frequency range by changing frequency for only a short period of time in order to probe different frequencies may be an acceptable solution to finding the global optimum frequency. However, in some applications even these short duration plasma disturbances are not acceptable. A solution for finding the global optimum with minimal disturbance of the plasma load is desired. In many applications finding the optimum operating frequency is equivalent to minimizing the load impedance mismatch, but other factors such as stability of the plasma system and efficiency of the system may factor into the optimality of a frequency.